You can view the offending commit here: 44dd073 There is not yet a fix in mind for these gamepads and adapters that don't appear to be reporting the analog values correctly. The fact that is 'worked' in a previous release of the Mupen64Plus core plugin is merely on accident, and didn't really 'work' - it would break analog in some games such as Golden Eye and others on gamepads that properly report the full range (see the extensive list of gamepads I tested above).
The problem is some adapters and devices are not reporting the full analog range, normalized from 0.0 to 1.0, so when the Mupen64Plus core receives the value and multiplies axisValue * 80 (0 - 80 is the range of N64 analog stick), it is not enough to move the stick where it ought to really be.
Please don't 'downgrade' the application - you will end up with more problems and doing that has nothing to do with solving this particular edge case.